Statistic quantitative qualitative sample

Introduction To
The Statistical
Concepts

Objectives
• Define statistics.
• Enumerate the importance and limitations of statistics.
• Explain the process of statistics.
• Know the difference between descriptive and inferential
statistics.
• Distinguish between qualitative and quantitative variables.
• Distinguish between discrete and continuous variables.
• Determine the level of measurement of variables.

Definition of Statistics
STATISTICS is the science of
collecting, organizing,
summarizing and analyzing
information to draw conclusions
or answer questions.

Definition of Statistics
1. Collection of information.
2. Organization and summarization of information.
3. Information is analyzed to draw conclusions or
answer specific questions.
4. Results should be reported using some measure
that represents how convinced we are that our
conclusions reflect reality.

It enables people to
make decisions based
on empirical evidence.
Importance of Statistics
Provides us with tools
needed to convert
massive data into
pertinent information
that can be used in
decision making.
Provides us
information that we
can used to make
sensible decision.

DATA
DATA are factual
information used as a basis
for reasoning, discussion, or
calculation.

Field of Statistics
Mathematical
Statistics
- The study and development of statistical theory
and methods in the abstract.
Applied Statistics
- The application of statistical methods to solve real
problems involving randomly generated data and
the development of new statistical methodology
motivated by real problems.

Limitation of Statistics
1. Statistics is not suitable
to the study of qualitative
phenomenon.
2. Statistics does not
study individuals.
3. Statistical laws are not
exact.
4. Statistics table may be
misused.
5. Statistics is only, one
of the methods of
studying a problem.

Process of Statistics
1. Identify the research objective
- A researcher must determine the
question(s) he or she wants to
answered. The question(s) must
clearly identify the population that is
to be studied.

2. Collect the information needed to
answer the questions.
- Conducting research on an entire
population is often difficult and
expensive, so we typically look at a
sample.

EXAMPLE
The Philippine Mental Health Associations contacts 1,
028 teenagers who are 13 to 17 years of age and live in
Laoag City and asked whether or not they had been
prescribed medications for any mental disorders, such as
depression or anxiety.
Population:
Teenagers 13 to 17
years of age who live in
Laoag City.
Sample:
1, 028 teenagers 13
to 17 years of age who live
in Laoag City.

EXAMPLE
A farmer wanted to learn about the weight of
his corn crop. He randomly sampled 100 plants and
weighted the corn on each plant.
Population:
Entire corn crop
Sample:
100 selected
corn crop

3. Organize and summarize the
information
- Descriptive statistics allow the
researcher to obtain an overview of the
data and can help determine the type of
statistical methods the research should
use.

4. Draw conclusion from the
information
- Information collected from the sample is
generalized to the population.
- Inferential statistics uses methods.

Take Note!
If the entire population is
studied, then inferential statistics
is not necessary, because
descriptive statistics will provide
all the information that we need
regarding the population.

EXAMPLE
1. A badminton player wants to
know his average score for the
past 10 games.

EXAMPLE
2. A car manufacturer wishes to
estimate the average lifetime of
batteries by testing a sample of 50
batteries.

EXAMPLE
3. Janine wants to determine the
variability of her six exam scores in
Algebra.

EXAMPLE
4. A politician wants to determine
the total number of votes his rival
obtained in the past election
based on his copies of the tally
sheet of electoral returns.

EXAMPLE
5. A shipping company wishes to
estimate the number of
passengers traveling via their
ships next year using their data on
the number of passengers in the
past three years.

Distinction Between
Qualitative and
Quantitative
Variables

Qualitative and Quantitative Variables
- Characteristics of the
individuals within the
population.
Variables

- is variable that yields
categorical responses. It is a
word or a code that represents
a class or category.
Qualitative Variable

- takes on numerical values
representing an amount or
quantity.
Quantitative Variable

EXAMPLE
1. Hair Color
2. Temperature
3. Stages of Breast Cancer
4. Number of Hamburger Sold

EXAMPLE
5. Number of Children
6. Zip Code
7. Place of Birth
8. Degree of Pain

Distinction Between
Discrete and
Continuous

Discrete and Continuous
- is a quantitative variable
that either a finite number of
possible values or a countable
number of possible values.
Discrete Variable

Discrete and Continuous
- is a quantitative variable
that has an infinite number of
possible values that are not
countable.
Continuous Variable

EXAMPLE
1. The number of heads obtained after flipping a
coin five times.
2. The number of cars that arrive at a McDonald’s
drive-through between 12:00 P.M. and 1:00 P.M.
3. The distance of a 2005 Toyota Car can travel in
city conditions with a full tank of gas.

EXAMPLE
4. Number of words correctly spelled.
5. Time of a runner to finish one
lap.

Levels of Measurement
Nominal
Ordinal
Interval
Ratio
Quantitative
Qualitative

Nominal
- They are sometimes called
categorical scales or categorical data.
Such a scale classifies persons or
objects into two or more categories.

Example
Nominal
Method of Payment
Type of School
Eye Color

Ordinal
- This involves data that may be
arranged in some order, but
differences between data values
either cannot be determined or
meaningless.

Example
Food Preferences
Stage of Diseases
Social Economic Class
Severity of Pain
Ordinal

- This is a measurement level not only
classifies and orders the measurement, but it
also specifies that the distances between
each interval on the scale are equivalent
along the scale from low interval to high
interval.
Interval

Example
• Temperature on Fahrenheit/Celsius
Thermometer
• Trait Anxiety
• IQ
Interval

- A ratio scale represents the highest,
most precise, level of measurement. It has the
properties of the interval level of
measurement and the ratios of the values of
the variable have meaning.
Ratio

Example
• Height and Weight
• Time
• Time until death
Ratio

Scales Counting Ranking
Addition/
Subtraction
Multiplication/
Division
Nominal √
Ordinal √ √
Interval √ √ √
Ratio √ √ √ √

Example
1. Ranking of college athletic teams.
2. Employee number.
3. Number of vehicles registered.
4. Brands of soft drinks.
5. Number of car passers along C5 on a
given day.

Identify each of the following data sets as
either Population or a Sample.
1. The grade point average (GPAs) of all students at a
college.
2. The GPAs of a randomly selected group of students at
a college campus.
3. The ages of the nine Supreme Court Justice of the
United States on January 1, 1842.
4. The gender of every second customer who enter a
movie theater.
5. The lengths of Atlantic croakers caught on a fishing trip
to the beach.

Identify the following measures as either
Quantitative or Qualitative.
1. The gender of the first 40 newborns in a hospital
one year.
2. The natural hair color of 20 randomly selected
fashion models.
3. The ages of 20 randomly selected fashion models.
4. The fuel economy in miles per gallon of 20 new
cars purchased last month.
5. The political affiliation of 500 randomly selected
voters.

Data Collection and
Basic Concepts in
Sampling Design

Objectives
• Determine the sources of data (primary and
secondary data).
• Distinguish the different methods data
collection under primary and secondary data.
• Determine the appropriate sample size.
• Differentiative various sampling techniques.
• Know the sources of errors in sampling.

Data Collection
Data collection is the process of
gathering and measuring information
on variables of interest, in an
established systemic fashion that
enables one to answer stated research
questions, test hypotheses, and
evaluate outcomes.

Consequences
from Improperly
Collected Data

Data Collection
• Inability to answer research questions accurately.
• Inability to repeat and validate the study.
• Distorted findings resulting in wasted resources.
• Misleading other researches to pursue fruitless
avenues of investigation.
• Compromising decisions for public policy.
• Causing harm to human participants and animal
subjects.

Steps in Data Gathering
1. Set the objectives for collecting data.
2. Determine the data needed based on the set
objectives.
3. Determine the method to be used in data
gathering and define the comprehensive data
collection points.
4. Design data gathering forms to be used.
5. Collect data.

Choosing of
Method of Data
Collection

Data Collection
Decision-makers need
information that is relevant, timely,
accurate and usable. The cost of
obtaining, processing and
analyzing these data is high.

Primary Sources
Provide a first-hand
account of an event or time
period and are considered to
be authoritative.

Primary Data
Data documented by the
primary source. The data
collectors documented the
data themselves.

Secondary Sources
Offer an analysis,
interception or a restatement
of primary sources and are
considered to be persuasive.

Secondary Data
Data documented by a
secondary source. The data
collectors had the data
documented by other
sources.

The Primary Data
Can Be Collected In
5 Methods

Methods
1. Direct Personal Interviews
- the researcher has direct
contact with the interviewee. The
researcher gathers information by
asking questions to the interviewee.

Methods
2. Interact/Questionnaire Method
- this methods of data collection
involve sourcing and accessing
existing data that were originally
collected for the purpose of the study.

Questions to be Considered
Who exactly do we want to know
according to the objectives and
variables we identified earlier?

Of whom will we ask
questions and what
techniques will we use?

Are our informants
mainly literate or
illiterate?

How large is the
sample that will be
interviewed?

Key Design
Principles of a
Good
Questionnaire

Key Design Principles of a Good Questionnaire
1. Keep the questionnaire as short as
possible.
2. Decide on the type of questionnaire
(open ended or closed ended).
3. Write the questions properly.
4. Order the questions appropriately.

5. Avoid questions that prompt or motivate
the respondent to say what you would like
to hear.
6. Write an introductory letter or an
introduction.
7. Write special instructions for
interviewers or respondents.

8. Translate the questions if
necessary.
9. Always test your questions
before taking the survey.

Open-Ended
Question & Closed-
ended Question

Open-ended Question
- type of question that does
not include response categories.
The respondent is not given any
possible answers to choose
from.

Closed-ended Question
- is a type of question that
includes a list of response
categories from which
respondent will select his/her
answer.

Open-ended VS Closed-ended
• More detailed
answer.
• Could reveal
additional
insights.
• Easy to encode,
tabulate, and
analyze.
• Easy to understand.
• Enables inter-study
comparison.
• Saves time and
money.
• High response rate.

Open-ended VS Closed-ended
• Difficult to encode,
tabulate, and analyze.
• Low response rate.
• Respondent has to be
articulate.
• Respondent could feel
threatened.
• Responses could have
different levels of
detail.
• Could frustrate
respondents.
• Potentially biased
response sets.
• Difficult or impossible
to detect if
respondent truly
understood the
questions.

Methods
3. Focus Group
- is a group interview of
approximately six to twelve people
who share similar characteristics or
common interest.

Methods
4. Experiment
- is a method of collecting data
where there is direct human
intervention on the conditions that
may affect the values of the variable
of interest.

Experiment
• Ethical, moral, and legal
concerns.
• Unrealistic controlled
environments.
• Inability to control for all
variables.

Methods
5. Observation
- is a technique that involves
systematically selecting, watching and
recording behaviors of people or other
phenomena and aspects of the setting
in which they occur, for the purpose of
getting specified information.

Observation
• Radiographic
• Biochemical
• Xray machines
• Microscope
• Clinical examinations
• Microbiological examinations

The Secondary
Data Can Be
Collected In 5
Methods

Methods
1. Published report on newspaper and
periodicals.
2. Financial data reported in annual
reports.
3. Records maintained by the institution.
4. Internal reports of the government
departments.
5. Information from official publications.

Take Note!
• Always investigate the validity and reliability of
the data by examining the collection method
employed by your source.
• Do not use inappropriate data for your
research.
• The choice of methods of data collection is
largely based on the accuracy of the
information they yield.

Sample Size
“How many
participants should
be chosen for a
survey”?

Sample Size
- is typically denoted by n and
it is always a positive integer.
- no exact sample size can be
mentioned here and it can vary in
different research settings.

Take Note!
• Representativeness, not size, is the
more important consideration.
• Use no less than 30 subjects if possible.
• If you use complex statistics, you may
need a minimum of 100 or more in your
sample (varies with method)

Non-Statistical
and Statistical
Considerations

Non-Statistical Considerations
- It may include availability
of resources, man power,
budget, ethics and sampling
frame.

Statistical Considerations
- It will include the
desired precision of the
estimate.

Criteria in
Determining
the Appropriate
Sample Size

1. Level of Precision
- Also called sampling
error, the level of precision, is
the range in which the true
value of the population is
estimated to be.

2. Confidence Interval
- It is statistical measure of
the number of times out of
100 that results can be
expected to be within a
specified range.

2. Confidence Interval
Desired Confidence
Level
Z-Score
80% 1.28
85% 1.44
90% 1.65
95% 1.96
99% 2.58

3. Degree of Variability
- depending upon the
target population and
attributes under
consideration, the degree of
variability varies considerably.

Methods in
Determining
the Sample Size

1. Estimate the Mean or
Average
- The sample size required
to estimate the population
mean µ to with a level of
confidence with specified
margin of error e.

Take Note!
If when is unknown, it is common practice
to conduct a preliminary survey to
determine and use it as an estimate of or
use results from previous studies to obtain
an estimate of . When using this approach,
the size of the sample should be at least
30.

Example
A soft drink machine is regulated so that the
amount of drink dispensed is approximately
normally distributed with a standard
deviation equal to 0.5 ounce. Determine the
sample size needed if we wish to be 95%
confident that our sample mean will be
within 0.03 ounce from the true mean.

2. Estimating Proportion (Infinite
Population)
- The sample size required
to obtain a confidence interval
for p with specified margin of
error e.

Example
Suppose we are doing a study on the inhabitants
of a large town, and want to find out how many
households serve breakfast in the mornings. We
don’t have much information on the subject to
begin with, so we’re going to assume that half of
the families serve breakfast: this gives us
maximum variability. So p = 0.5. We want 99%
confidence and at least 1% precision.

3. Slovin’s Formula
- Slovin’s formula is used
to calculate the sample size n
given the population size and
error.

Example
A researcher plans to conduct a
survey about food preference of
BS Stat students. If the population
of students is 1000, find the
sample size if the error is 5%

4. Finite Population
Correction
- If the population is
small then the sample size
can be reduced slightly.

Online Calculator of Sample
Size
https://select-statistics.co.uk/calculato
rs/sample-size-calculator-population-
proportion/
https://www.calculator.net/sample-siz
e-calculator.html

Reason for Sampling
• Important that the individuals included
in sample represent a cross section
individuals in the population.
• If sample is not representative it is
biased. You cannot generalize to the
population from your statistical data.

Observation Unit
• An object on which a
measurement is taken. This
is the basic unit of
observation, sometimes
called an element.

Target Population
• The complete
collection of
observation we want to
study.

Sample Population
• The collection of all possible
observation units that might
have been chosen in a
sample; the population from
which the sample was taken.

Sample
• A subset of a
population.

Sampling Unit
• A unit that can be selected for a
sample. We may want to study
individuals, but do not have a
list of all individuals in the target
population.

Sampling Frame
• A list, map, or other
specification of sampling
units in the population from
which a sample may be
selected.

Sampling Bias
• This involves problems in
your sampling, which reveals
that your sample is not
representative of your
population.

Advantages of
Sampling Over
Complete
Enumeration

Advantage of Sampling
• Less Labor
• Reduced Cost
• Greater Speed
• Greater Scope
• Greater Efficiency and Accuracy
• Convenience
• Ethical Considerations

1. Probability Sample
• Samples are obtained using some
objective chance mechanism, thus
involving randomization.
• They require the use of a complete
listing of the elements of the
universe called sampling frame.

1. Non -Probability
Sample
• Samples are obtained haphazardly,
selected purposively or are taken as
volunteers.
• The probabilities of selection are
unknown.
• They should not be used for statistical
inference.

Sampling Procedure
• Identify the population
• Determine if population is accessible
• Select a sampling method.
• Choose a sample that is representative of
the population.
• Ask the question, can I generalize to the
general population from the accessible
population?

Basic Sampling
Technique of
Probability Sampling

1. Simple Random Sampling
• Most basic method of drawing a
probability sample.
• Assigns equal probabilities of
selection to each possible sample.
• Results to a simple random
sample.

Simple Random Sampling
Advantages and Disadvantages
• It is very
simple and
easy to
use.
• The sample
chosen may be
distributed over
a wide
geographic
area.

When to Use
Simple Random Sampling
• This is preferable to use if
the population is not
widely spread
geographically.

2. Systematic Random Sampling
• It is obtained by selecting every
kth individual from the
population.
• The first individual selected
corresponds to a random
number between 1 to n.

Obtaining a
Systematic
Random Sample

Obtaining a Systematic
Random Sample
• Decide on a method of
assigning a unique serial
number, from 1 to N, to each
one of the elements in the
populations.

Random Sample
• Compute for the sampling
interval:

Random Sample
• Select a number, from 1 to k, using a
randomization mechanism. The
element in the population assigned to
this number is the first elements of the
sample are those assigned to the
numbers and so on until you get a
sample of size.

Example
We want to select a sample
of 50 students from 500
students under this method kth
item and picked up from the
sampling frame.

Systematic Random Sampling
• Drawing of the
sample is easy. It is
easy to administer
in the field, and the
sample is spread
evenly over the
population.
• May give poor
precision when
unsuspected
periodicity is
present in the
population.

When to Use
Systematic Random Sampling
• This is advisable to us if the
ordering of the population is
essentially random and when
stratification with numerous
data is used.

3. Stratified Random
Sampling
• It is obtained by separating the
population into non-overlapping
groups called strata and then
obtaining a simple random
sample from each stratum.

Example
A sample of 50 students is to be
drawn from a population consisting of 500
students belonging to two institutions A
and B. The number of students in the
institution A is 200 and the institution B is
300. How will you draw the sample using
proportional allocation?

Stratified Random Sampling
• Stratification of
respondents is
advantageous in
terms of precision
of the estimates of
the characteristics
of the population.
• Values of the
stratification variable
may not be easily
available for all units in
the population
especially if the
characteristics of
interest is homogenous.

When to Use
Stratified Random Sampling
• If the population is such that the
distribution of the characteristics of
the respondents under
consideration concentrated in
small and spread segment of the
population.

4. Cluster Sampling
• You take sample from naturally
occurring groups in your population.
• The clusters are constructed such that
the sampling units are heterogeneous
within the cluster and homogeneous
among the clusters.

Obtaining a Cluster Sample
• Divide the population into non-
overlapping clusters.
• Number the clusters in the
population from 1 to N.

Obtaining a Cluster Sample
• Select n distinct numbers from 1 to
N using a randomization
mechanism. The selected clusters
are the clusters associated with the
selected numbers.
• The sample will consist of all
elements in the selected clusters.

Example
A researcher wants to
survey academic performance
of high school students in
MIMAROPA.

Cluster Sampling
• There is no need to
come out with a list
of units in the
population; all what
is needed is simply
a list of the clusters.
• In actual field
applications adjacent
households tend to
have more similar
characteristics than
households distantly
apart.

When to Use
Cluster Sampling
• If the population can be grouped
into clusters where individual
population elements are known to
be different with respect to the
characteristics under study, this
preferable to use.

5. Multi-Stage Sampling
• Selection of the sample is done in two
or more steps or stages, with sampling
units varying in each stage.
• The population is first divided into
number of first-stage sampling units
from which a sample is drawn.

Obtaining a
Multi-Stage Sampling

Obtaining a Multi-Stage Sampling
• Organize the sampling process into
stages where the unit of analysis is
systematically grouped.
• Select a sampling technique for each.
• Systematically apply the sampling
technique to each stage until the unit of
analysis has been selected.

Example
Suppose we wish to study the
expenditure patterns of households in
NCR. We can select a sample of
households for this study using
simple three-stage sampling.

• It is easier to generate
adequate sampling
frames. Transportation
costs are greatly
reduced since there is
some form of
clustering among
ultimate or final
samples.
• It is complexity in
theory may be difficult
to apply in the field.
Estimation
procedures may be
difficult for non-
statisticians to follow.

When to Use
• If no population list is
available and if the
population covers a wide
area.

Take Note!
• Used probability sampling if the
main objective of the sample
survey is making inferences
about the characteristics of
the population under study.

Basic Sampling
Technique of Non-

Accidental Sampling
• There is no system of
selection but only those
whom the researcher or
interviewer meets by chance.

Quota Sampling
• There is specified number
of persons of certain
types is included in the
sample.

Convenience Sampling
• It is process of picking out
people in the most
convenient and fastest way
to get reactions immediately.

Purposive Sampling
• It is based on certain
criteria laid down by the
researcher.

Judgement Sampling
• Selects sample in
accordance with an
expert’s judgement.

Cases wherein Non-
is Useful

Cases wherein Non-Probability
Sampling is Useful
• Only few are willing to be interviewed.
• Extreme difficulties in locating or
identifying subjects.
• Probability sampling is more expensive
to implement.
• Cannot enumerate the population
elements.

1. Non-sampling Error
• Errors that results from the
survey process.
• Any errors that cannot be
attributed to the sample-to-
sample variability.

Sources of Non-sampling Error
• Non-response
• Interview Error
• Misrepresented Answers
• Data entry errors
• Questionnaire Design
• Wording of Questions
• Selection Bias

2. Sampling Error
• Error that results from taking one
sample instead of examining the
whole population.
• Error that results from using
sampling to estimate information
regarding a population.

Statistic quantitative qualitative sample

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